Finite Group Databasebeta

← #37545346

Subgroups — #37545346

Order 23168.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153843C211yesmaximal, characteristic, complemented
2#26041940C211yesmaximal, characteristic, complemented
3#26041917C211yesmaximal, characteristic, complemented
4#26041664C211yesmaximal, characteristic, complemented
5#26041534C211yesmaximal, characteristic, complemented
6#26041532C211yesmaximal, characteristic, complemented
7#26041503C211yesmaximal, characteristic, complemented
8#26041496C211yesmaximal, characteristic, complemented
9#26041440C211yesmaximal, characteristic, complemented
10#26041428C211yesmaximal, characteristic, complemented
11#26041424C211yesmaximal, characteristic, complemented
12#26041418C211yesmaximal, characteristic, complemented
13SD16×Dic181C211yesmaximal, characteristic, complemented
14#26041355C211yesmaximal, characteristic, complemented
15C2×#137×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18#19153843—24no—
19C2×#15668436C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic, complemented
22C2×D1448C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24C2×#15668432C2211yescharacteristic
25#19153805—21no—
26#19153805C2211yescharacteristic
27#19153805C2211yescharacteristic, complemented
28#19153799—21no—
29#19153792—21no—
30#19153792C2211yescharacteristic
31#19153792C2211yescharacteristic
32#19153790—21no—
33#19153790C2211yescharacteristic
34#19153790C2211yescharacteristic, complemented
35#19153788—21no—
36#19153784—21no—
37Q8×Dic181C2211yescharacteristic, complemented
38D4×Dic181C2211yescharacteristic
39C4×C22⋊D181—21no—
40C4×C22⋊D181C2211yescharacteristic
41C2×#15668426—21no—
42#19153748C2211yescharacteristic, complemented
43#19153745C2211yescharacteristic, complemented
44#19153740C2211yescharacteristic, complemented
45#19153740C2211yescharacteristic, complemented
46#19153740C2211yescharacteristic, complemented
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic, complemented
49#19153737C2211yescharacteristic
50C22⋊#13089678C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic
52C8×Dic181C2211yescharacteristic, complemented
53C2×#41×C181C2211yescharacteristic
54C22×Q8×C181C2211yescharacteristic, complemented
55#137×C181—24no—
56C2×Q16×C181C2211yescharacteristic, complemented
57C2×Q16×C181C2211yescharacteristic, complemented
58C2×SD16×C181C2211yescharacteristic
59C2×SD16×C181C2211yescharacteristic
60C2×M16×C181C2211yescharacteristic, complemented
61C23×D181—21no—
62#15668450—22no—
63#15668450—41no—
64C2×D724—21no—
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181D411yescharacteristic
71D4×D181—22no—
72D4×D181—41no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668436—22no—
77#15668436—41no—
78#15668436—41no—
79D1448—22no—
80#15668434—22no—
81#15668432—22no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426—21no—
100#15668426D411yescharacteristic
101C4×Dic181—21no—
102C4×Dic181C2311yescharacteristic
103#41×C181—22no—
104#41×C181—41no—
105C2×Q8×C181—21no—
106C2×Q8×C181—22no—
107C2×Q8×C181—41no—
108C2×Q8×C181C2311yescharacteristic
109C2×Q8×C181C2311yescharacteristic
110C2×Q8×C181C2311yescharacteristic
111C2×D4×C181—21no—
112C2×D4×C181C2311yescharacteristic
113C22×C4×C181—21no—
114C22×C4×C181—21no—
115C22×C4×C181C2311yescharacteristic
116Q16×C181—22no—
117Q16×C181—22no—
118SD16×C181—22no—
119SD16×C181D414yescomplemented
120M16×C181—22no—
121C2×C8×C181C2311yescharacteristic
122C2×C8×C181C2311yescharacteristic
123C22×D181—21no—
124C22×D181—21no—
125C22×D181—42no—
126C22×D181—42no—
127C22×D181—81no—
128C22×D181C2×D411yescharacteristic
129D724—21no—
130D724—21no—
131D724—21no—
132D724—21no—
133D724—42no—
134C22⋊D181—41no—
135C22⋊D181—42no—
136C22⋊D181—42no—
137C22⋊D181—81no—
138C2×Dic181—21no—
139C2×Dic181—21no—
140C2×Dic181—81no—
141C2×Dic181C2×D411yescharacteristic
142C2×Dic181C2×D411yescharacteristic
143C2×Dic181C2×D411yescharacteristic
144C4×D181—21no—
145C4×D181—21no—
146C4×D181—42no—
147#13089678—21no—
148#13089678—21no—
149C23×C181—21no—
150C23×C181C2×D411yescharacteristic
151Q8×C181—21no—
152Q8×C181—21no—
153Q8×C181—21no—
154Q8×C181—21no—
155Q8×C181—21no—
156Q8×C181—42no—
157Q8×C181C2×D412yes—
158D4×C181—21no—
159D4×C181—42no—
160D4×C181C2×D412yes—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181—21no—
164C2×C4×C181—21no—
165C2×C4×C181—21no—
166C2×C4×C181—42no—
167C2×C4×C181—42no—
168C2×C4×C181C2×D411yescharacteristic
169C2×C4×C181C2411yescharacteristic
170C8×C181—21no—
171C8×C181C2×D412yes—
172C22×C181—21no—
173C22×C181—22no—
174C22×C181—21no—
175C22×C181—21no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181C22×D411yescharacteristic
179C2×D181—21no—
180C2×D181—21no—
181C2×D181—21no—
182C2×D181—41no—
183C2×D181—41no—
184C2×D181—41no—
185C2×D181—41no—
186C2×D181—41no—
187C2×D181—41no—
188C2×D181—84no—
189C4×C181—21no—
190C4×C181—22no—
191C4×C181—41no—
192C4×C181—41no—
193C4×C181C22×D411yescharacteristic
194C4×C181H(5,𝔽2)11yescharacteristic
195Dic181—21no—
196Dic181—21no—
197Dic181—21no—
198Dic181—41no—
199Dic181—41no—
200C2×C181—42no—
201C2×C181—41no—
202C2×C181D4211yescharacteristic
203C2×C181#57511yescharacteristic
204C2×C181#57711yescharacteristic
205D181—41no—
206D181—81no—
207D181—81no—
208C181#327511yescharacteristic, complemented, Sylow
209#3275—1811nomaximal, Sylow
210C2×#137D18111yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—1811no—
212#548—1811no—
213#546—1811no—
214#495—1811no—
215#470—1811no—
216#469—1811no—
217#464—1811no—
218#463—1811no—
219#452—1811no—
220#450—1811no—
221#449—1811no—
222#448—1811no—
223C4×SD16—1811no—
224#436—1811no—
225C2×#41—1811no—
226C2×#41C2×D18111yescharacteristic
227C22×Q8C2×D18111yescharacteristic, complemented
228C22×D4—1811no—
229#137—24no—
230AGL(1,ℤ/8)—3624no—
231C2×Q16C2×D18111yescharacteristic, complemented
232C2×Q16C2×D18111yescharacteristic, complemented
233C2×SD16—1811no—
234C2×SD16—1811no—
235C2×SD16—1811no—
236C2×SD16C2×D18111yescharacteristic
237C2×SD16C2×D18111yescharacteristic
238C2×D8—1811no—
239C2×D8—1811no—
240C2×M16—1811no—
241C2×M16C2×D18111yescharacteristic, complemented
242#124—3621no—
243#124—1811no—
244#124—1811no—
245#123—3621no—
246C22⋊Q8—3621no—
247C22⋊Q8—1811no—
248C22⋊Q8—1811no—
249#121—3621no—
250#121—3621no—
251#121—1811no—
252#121—1811no—
253#120—3621no—
254C4×Q8—1811no—
255C4×D4—3621no—
256C4×D4—1811no—
257C4×D4—1811no—
258C2×C22⋊C4—3621no—
259#106—1811no—
260C4⋊C8—1811no—
261#103—1811no—
262#103—1811no—
263#103—1811no—
264#102—1811no—
265#102—1811no—
266#102—1811no—
267C22⋊C8—1811no—
268C22⋊C8—1811no—
269C4×C8—1811no—
270C24—3621no—
271#41—22no—
272#41—41no—
273#41—3622no—
274#41—7241no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D18111yescharacteristic
279C2×Q8C22×D18111yescharacteristic
280C2×Q8C22×D18111yescharacteristic
281C2×D4—21no—
282C2×D4—3621no—
283C2×D4—3622no—
284C2×D4—3621no—
285C2×D4—3621no—
286C2×D4—3621no—
287C2×D4—1811no—
288C2×D4—1811no—
289C2×D4—1811no—
290C2×D4—7241no—
291C2×D4C22×D18111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—3621no—
295C22×C4—3621no—
296C22×C4—1811no—
297C22×C4C22×D18111yescharacteristic
298Q16—22no—
299Q16—22no—
300SD16—22no—
301SD16—3622no—
302SD16—7241no—
303SD16—7241no—
304SD16C22⋊D18114yescomplemented
305D8—3622no—
306D8—3622no—
307M16—22no—
308M16—3622no—
309C2×C8—1811no—
310C2×C8—1811no—
311C2×C8C22×D18111yescharacteristic
312C2×C8C22×D18111yescharacteristic
313C4⋊C4—3621no—
314C4⋊C4—3621no—
315C4⋊C4—3621no—
316C4⋊C4—1811no—
317C4⋊C4—1811no—
318C4⋊C4—1811no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—3621no—
323C22⋊C4—3621no—
324C22⋊C4—3621no—
325C22⋊C4—3621no—
326C22⋊C4—3621no—
327C22⋊C4—3621no—
328C22⋊C4—1811no—
329C22⋊C4—1811no—
330C42—3621no—
331C42—1811no—
332C23—21no—
333C23—3621no—
334C23—3621no—
335C23—14481no—
336C23—1811no—
337C23—7242no—
338C23—7242no—
339C23D4×D18111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D18112yes—
347D4—21no—
348D4—42no—
349D4—3621no—
350D4—3621no—
351D4—3621no—
352D4—3621no—
353D4—14481no—
354D4—7242no—
355D4—7241no—
356D4—7242no—
357D4—7242no—
358D4C2×C22⋊D18112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—3621no—
367C2×C4—3621no—
368C2×C4—3621no—
369C2×C4—3621no—
370C2×C4—14481no—
371C2×C4—1811no—
372C2×C4—1811no—
373C2×C4—1811no—
374C2×C4—7242no—
375C2×C4D4×D18111yescharacteristic
376C2×C4C23×D18111yescharacteristic
377C8—21no—
378C8—3621no—
379C8—3621no—
380C8C2×C22⋊D18112yes—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—3621no—
388C22—3621no—
389C22—3621no—
390C22—14484no—
391C22—7241no—
392C22—7241no—
393C22—7241no—
394C22—7241no—
395C22—7241no—
396C22—7241no—
397C22C2×D4×D18111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—3621no—
403C4—3621no—
404C4—3621no—
405C4—7241no—
406C4—7241no—
407C4C22×C22⋊D18111yescharacteristic
408C4#1915386111yescharacteristic
409C2—41no—
410C2—42no—
411C2—14481no—
412C2—14481no—
413C2—7241no—
414C2D4×C22⋊D18111yescharacteristic
415C2#2604207811yescharacteristic
416C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#137×C181C2
socleC22×C181C22×D4
hypercenterC2×#137D181
hypocenterC181#3275
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19153843C2semidirect
2. #26041940C2semidirect
3. #26041917C2semidirect
4. #26041664C2semidirect
5. #26041534C2semidirect
6. #26041532C2semidirect
7. #26041503C2semidirect
8. #26041496C2semidirect
9. #26041440C2semidirect
10. #26041428C2semidirect
11. #26041424C2semidirect
12. #26041418C2semidirect
13. SD16×Dic181C2semidirect
14. #26041355C2semidirect
15. C2×#137×C181C2semidirect
21. C2×#15668436C22semidirect
27. #19153805C22semidirect
34. #19153790C22semidirect
37. Q8×Dic181C22semidirect
42. #19153748C22semidirect
43. #19153745C22semidirect
44. #19153740C22semidirect
45. #19153740C22semidirect
46. #19153740C22semidirect
48. #19153738C22semidirect
50. C22⋊#13089678C22semidirect
52. C8×Dic181C22semidirect
54. C22×Q8×C181C22semidirect
56. C2×Q16×C181C22semidirect
57. C2×Q16×C181C22semidirect
60. C2×M16×C181C22semidirect
119. SD16×C181D4semidirect
208. C181#3275semidirect
210. C2×#137D181semidirect
227. C22×Q8C2×D181semidirect
231. C2×Q16C2×D181semidirect
232. C2×Q16C2×D181semidirect
241. C2×M16C2×D181semidirect
304. SD16C22⋊D181semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191538432
#260419402
#260419172
#260416642
#260415342
#260415322
#260415032
#260414962
#260414402
#260414282
#260414242
#260414182
SD16×Dic1812
#260413552
C2×#137×C1812
#3275181